Higman's conjecture on the number of conjugacy classes of \(U(n,q)\)

Igor Pak (UCLA)

Frank Adams 1,

In 1960, Higman asked whether the number \(f(n,q)\) of conjugacy classes of \(n\times n\) unitriangular matrices \(U(n,q)\) over the finite field with \(q\) elements, is polynomial in \(q\) for every \(n\). I will survey what is known about this problem and explain the connections to enumerative combinatorics and group representation theory. I will then describe our recent efforts to prove the conjecture for small \(n\) and disprove it for large \(n\). (Joint work with Andrew Soffer.)

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